Love the double feature here! Been considering going back and relearning analysis (whenever I can find the time) to strengthen my fundamentals. This one may provide some extra guidance I think. Also I picked up Differential Forms by Collier and am looking forward to digging into it! Keep up the great work
It's a great book, for sure. I'm so happy to hear that you got the Collier book. I really hope you enjoy it. Thank you for sharing that. Comments like yours really make uploading worth it.
Thank you for another excellent review! The Binmore book would be worth getting for me since I took a first course in analysis in 2019 and it would help me review before I take a second analysis course as a Master's student. I bought the Alcock book before but would need to skim that and maybe the Velleman book since I am still very shaky with proofs.
Thank you for the nice words. I'm glad you found it useful. Reviewing your proofs sounds wise! I felt very shaky with proofs, too, when I was getting back into math. Good luck with that analysis course. Let me know if you ever need some resources!
Thank you for giving this book recommendation. Analysis has been a subject that has scared me because of what a lot of people say about it being this absurdly hard field in mathematics. But I think it’s also the fact that a lot of Analysis pedagogy is mostly derived from Rudin’s book and many students not having proper preparation for the subject. Which is definitely a fault of mathematics education. Not to say Rudin’s book is bad, it’s a classic for a reason. But it’s for a specific audience and would not work well to teach everyone Analysis the first time around. Especially if one’s only prior experience with proof writing was an intro-level linear algebra course and an intro to proofs/discrete math course.
You can do it! My advice is to become very familiar with proof methods before attempting a proof based math course. I know it's not exciting, but it will pay off. I struggled a lot when getting back into math because my background in logic and proofs was shaky. I agree 100% with your thoughts on Rudin. It's a shame that Rudin is pushed onto students as a first option. It definitely warrants being mentioned, but so do so many other books. Thank you for sharing your perspective and thoughts.
Thanks. 🙂 I actually have a Spivak-type Calculus book I want to go through now that I have Calculus 1-3, Discrete Math, Linear Algebra, and ODE’s under my belt.. It’s called ‘Calculus Deconstructed’ by Zbignew Nitecki. It’s not as comprehensive as Spivak’s book but it’s similar in difficulty level. Just more structured around the sequencing of topics in a first semester analysis course rather than the elementary calculus sequence. So basic properties of real numbers. sequences, continuity, differentiation, integration, and series. It’s from MMA textbooks so it’s a fairly decent price. It might be worthwhile to review at some point just to give an idea of the different ‘Honors Calculus’ type books out there.
@@SabrinaMarquez-rw2xb Have you looked at J.A. Fridy, Introductory analysis: The theory of calculus, 2nd ed., Harcourt Academic Press, San Diego, CA, 2000? Aside from a significant typo near the beginning, it wasn't a bad book. It was also affordable. Unfortunately, I don't see a newer edition.
Thanks! If you're looking for more books on analysis, you can also try the ones by Ross, Zorn, Ash, Bartle and Sherbert. That's all I can recall off the top of my head! Thank you for commenting!
Love the double feature here! Been considering going back and relearning analysis (whenever I can find the time) to strengthen my fundamentals. This one may provide some extra guidance I think. Also I picked up Differential Forms by Collier and am looking forward to digging into it! Keep up the great work
It's a great book, for sure.
I'm so happy to hear that you got the Collier book. I really hope you enjoy it. Thank you for sharing that.
Comments like yours really make uploading worth it.
Wow - I used exactly that edition in 1988 at Nottingham University in the Uk
Wow, that's so cool! What did you and your fellow students think about it at the time?
Thank you for sharing!
Thank you for another excellent review! The Binmore book would be worth getting for me since I took a first course in analysis in 2019 and it would help me review before I take a second analysis course as a Master's student. I bought the Alcock book before but would need to skim that and maybe the Velleman book since I am still very shaky with proofs.
Thank you for the nice words. I'm glad you found it useful.
Reviewing your proofs sounds wise! I felt very shaky with proofs, too, when I was getting back into math.
Good luck with that analysis course. Let me know if you ever need some resources!
Thank you for giving this book recommendation. Analysis has been a subject that has scared me because of what a lot of people say about it being this absurdly hard field in mathematics. But I think it’s also the fact that a lot of Analysis pedagogy is mostly derived from Rudin’s book and many students not having proper preparation for the subject. Which is definitely a fault of mathematics education. Not to say Rudin’s book is bad, it’s a classic for a reason. But it’s for a specific audience and would not work well to teach everyone Analysis the first time around.
Especially if one’s only prior experience with proof writing was an intro-level linear algebra course and an intro to proofs/discrete math course.
You can do it! My advice is to become very familiar with proof methods before attempting a proof based math course. I know it's not exciting, but it will pay off. I struggled a lot when getting back into math because my background in logic and proofs was shaky.
I agree 100% with your thoughts on Rudin. It's a shame that Rudin is pushed onto students as a first option. It definitely warrants being mentioned, but so do so many other books.
Thank you for sharing your perspective and thoughts.
Thanks. 🙂
I actually have a Spivak-type Calculus book I want to go through now that I have Calculus 1-3, Discrete Math, Linear Algebra, and ODE’s under my belt.. It’s called ‘Calculus Deconstructed’ by Zbignew Nitecki. It’s not as comprehensive as Spivak’s book but it’s similar in difficulty level. Just more structured around the sequencing of topics in a first semester analysis course rather than the elementary calculus sequence. So basic properties of real numbers. sequences, continuity, differentiation, integration, and series. It’s from MMA textbooks so it’s a fairly decent price. It might be worthwhile to review at some point just to give an idea of the different ‘Honors Calculus’ type books out there.
Thank you for bringing this book to my attention. This one looks really cool!! AMS/MAA puts out some really good stuff.
@@SabrinaMarquez-rw2xb Have you looked at J.A. Fridy, Introductory analysis: The theory of calculus, 2nd ed., Harcourt Academic Press, San Diego, CA, 2000? Aside from a significant typo near the beginning, it wasn't a bad book. It was also affordable. Unfortunately, I don't see a newer edition.
Great vid
Thanks! If you're looking for more books on analysis, you can also try the ones by Ross, Zorn, Ash, Bartle and Sherbert. That's all I can recall off the top of my head! Thank you for commenting!
Another great video. 🧮
Thank you, very much appreciated!